Preventing Twitter from Automatic Posting

Our site suddenly starting tweeting new posts automatically, which I do not want and did not intentionally turn on. I have googled and can find no way to turn this off. I am having to go to Twitter and delete the tweet the minute it appears which is obviously not a good system. :) Can anyone help? Thank you.

What I don't understand is... there are zillions of sites telling you how to ADD it.. but NONE telling you how to get rid of it LOL. I even deleted my entire Twitter icon and link but it is still auto-posting.

Once you’ve approved a connection to any of the below services, you’ll see a Publicize section in the Publish box on your post writing screen each time you write a new post.
If you don't want to do it with any post, you can edit it.